Transcript Page 292 HW Answers
Page 292 HW Answers
Our learning goal is to be able to solve for perimeter, area and volume.
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Circles
Learning Goal Assignments
Perimeter and Area of Rectangles and Parallelograms Perimeter and Area of Triangles and Trapezoids The Pythagorean Theorem Drawing Three-Dimensional figures Volume of Prisms and Cylinders Volume of Pyramids and Cones Surface Area of Prisms and Cylinders 9.
Surface Area of Pyramids and Cones 10. Spheres
Learning Goal Assignment Learn to find the area and circumference of circles.
Pre-Algebra
6-4 Circles
Pre-Algebra HOMEWORK
Page 298 #1-18
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Warm Up
1. Find the length of the hypotenuse of a right triangle that has legs 3 in. and 4 in. long.
5 in.
2. The hypotenuse of a right triangle measures 17 in., and one leg measures 8 in. How long is the other leg?
15 in.
3. To the nearest centimeter, what is the height of an equilateral triangle with sides 9 cm long?
8 cm
6-4 Circles
Problem of the Day
A rectangular box is 3 ft. by 4 ft. by 12 ft. What is the distance from a top corner to the opposite bottom corner?
13 ft
Pre-Algebra
Learning Goal Assignment Learn to find the area and circumference of circles.
Pre-Algebra
6-4 Circles
Vocabulary
circle radius diameter circumference
Pre-Algebra
6-4 Circles
A circle is the set of points in a plane that are a fixed distance from a given point, called the center. A radius connects the center to any point on the circle, and a diameter connects two points on the circle and passes through the center.
Pre-Algebra
6-4 Circles
Radius Center Diameter
The diameter d is twice the radius r.
d
= 2
r
Circumference The circumference of a circle is the distance around the circle.
Pre-Algebra
6-4 Circles Pre-Algebra
6-4 Circles Remember!
Pi ( p ) is an irrational number that is often approximated by the rational numbers 3.14 and .
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Pre-Algebra
6-4 Circles Additional Example 1: Finding the Circumference of a Circle Find the circumference of each circle, both in terms of
p
and to the nearest tenth. Use 3.14 for
p
.
A. Circle with a radius of 4 m C = 2 p
r
= 2 p (4) = 8 p m 25.1 m B. Circle with a diameter of 3.3 ft C = p
d
= p (3.3) = 3.3
p ft 10.4 ft
Pre-Algebra
6-4 Circles Try This: Example 1 Find the circumference of each circle, both in terms of
p
and to the nearest tenth. Use 3.14 for
p
.
A. Circle with a radius of 8 cm C = 2 p
r
= 2 p (8) = 16 p cm 50.2 cm B. Circle with a diameter of 4.25 in.
C = p
d
= p (4.25) = 4.25
p in. 13.3 in.
Pre-Algebra
6-4 Circles Pre-Algebra
6-4 Circles Additional Example 2: Finding the Area of a Circle Find the area of each circle, both in terms of
p
and to the nearest tenth. Use 3.14 for
p
.
A. Circle with a radius of 4 in.
A = p
r
2 = p ( 4 2 ) = 16 p in 2 50.2 in 2 B. Circle with a diameter of 3.3 m A = p
r
2 = p ( 1.65
2 ) = 2.7225
p m 2 8.5 m 2
d
2 = 1.65
Pre-Algebra
6-4 Circles Try This: Example 2 Find the area of each circle, both in terms of
p
and to the nearest tenth. Use 3.14 for
p
.
A. Circle with a radius of 8 cm A = p
r
2 = p ( 8 2 ) = 64 p cm 2 201.0 cm 2 B. Circle with a diameter of 2.2 ft A = p
r
2 = p ( 1.1
2 )
d
2 = 1.1
= 1.21
p ft 2 3.8 ft 2
Pre-Algebra
6-4 Circles Additional Example 3: Finding the Area and Circumference on a Coordinate Plane Graph the circle with center (–2, 1) that passes through (1, 1). Find the area and circumference, both in terms of
p
and to the nearest tenth. Use 3.14 for
p.
A = = p p
r
( 2 3 2 ) C = p
d
= p (6) = 9 p units 2 = 6 p units 28.3 units 2 18.8 units
Pre-Algebra
6-4 Circles Try This: Example 3 Graph the circle with center (–2, 1) that passes through (–2, 5). Find the area and circumference, both in terms of
p
and to the nearest tenth. Use 3.14 for
p.
y
(–2, 5) 4
x
A = p
r
2 = p ( 4 2 ) = 16 p units 2 50.2 units 2 C = p
d
= p (8) = 8 p units 25.1 units (–2, 1)
Pre-Algebra
6-4 Circles Additional Example 4: Measurement Application A Ferris wheel has a diameter of 56 feet and makes 15 revolutions per ride. How far would someone travel during a ride? Use for
p
.
C = p d = p (56) 22 7 (56)
Find the circumference.
22 7 56 1 176 ft The distance is the circumference of the wheel times the number of revolutions, or about 176 15 = 2640 ft.
Pre-Algebra
6-4 Circles
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Try This: Example 4 A second hand on a clock is 7 in long. What is the distance it travels in one hour? Use for
p
.
7 C = p d = 12 p (14)
Find the circumference.
22 7 (14) 22 7 14 1 44 in. 6 3 The distance is the circumference of the clock times the number of revolutions, or about 44 60 = 2640 in.
Pre-Algebra
6-4 Circles Lesson Quiz Find the circumference of each circle, both in terms of
p
and to the nearest tenth. Use 3.14 for
p
.
1. radius 5.6 m 11.2
p m; 35.2 m 2. diameter 113 m 113 p mm; 354.8 mm
Find the area of each circle, both in terms of
p
and to the nearest tenth. Use 3.14 for
p
.
3. radius 3 in.
9 p in 2 ; 28.3 in 2 4. diameter 1 ft 0.25
p ft 2 ; 0.8 ft 2
Pre-Algebra